Mathematical model



June 9, 1925.

' M. R. BROWN MATHEMATICAL MODEL 1 Filed July 50, 1924 /Nl/ENT'OR Maurice R Brown ATTOR EY pythagorean theorem,

Patented June 9, 1925 MAURICE R. BROWN, OF AMSTERDAM, NEW YORK.

MATHEMATICAL MODEL.

Application filed July 30, 192%. Serial No. 728,195.

To all 107mm may concern:

Be it known that 1, Manama R. BROWN, a citizen of the United States, residing at Amsterdam, in the county of Montgomery and State of New York, have invented a new and useful Mathematical Model, of which the following is a specification.

My invention relates to mathematical models, and more particularly to models by which the truth of certain geometric theorems may be readily demonstrated for any and all cases.

Geometry, as ordinarily taught, involves the study of static figures illustrating or demonstrating one particular case of a theorem, and it is impossible to illustrate by ordinary methods the infinite resultant Variations in functional values occurring from relative changes in the magnitudes of which the resulting values are functions. The and the theorem that any right triangle may be inscribed in a semi-circle, for example, are fundamentals of plane geometry which should be thoroughly understood by the student, and all cases of which are susceptible of practical demonstration by a working model.

The object of my invention, therefore, is to provide a mathematical model of cheap and simple construction, which may be eas ily operated, which will illustrate in a dynamic manner the resulting variations in the mathematical squares of the two legs of a right triangle as they may vary in relative length, and which will incidentally demonstrate that the locus of the vertex of a right triangle having a hypotenuse of fixed length as a base, is a semi-circle.

JVith this object in view, my invention consists in the novel combinations, arrangements, and cooperative .relations of the parts forming my model, one form of which is illustrated in the accompanying drawing, in which- Fig. 1 is a front elevation of my device; Fig. 2 is a front elevation showing the elements of my model in a slightly different relative position; and Fig. 3 is a plan view looking down on Fig. 2.

Referring to the drawing, 1' is the base of my device which may be of wood or any suitable material upon which the mechanism may be mounted. For the purpose of explaining my device, it will be assumed that the square, 2, having four sides, each two units, N, in length, is erected upon the base, although the actual erection while desirable is not essential. At the mid point of the opposite sides, 3 and 4, similar cranks, 5 and 6, which may be of stiff wire, are axially mounted in the base and have small loops or eyes, 7, formed in their extremities, and have operating arms, 8 and 9, respectively, behind the base, which .are preferably bent at right angles to the crank or arms, 5 and 6, substantially as shown. The length of the cranks, 5 and 6, between the axis of rotation and the eyes, 7, is one unit, N. In the center of the square, 2, a crank having rectangular-1y disposed arms, 10 and 11, is axially mounted in the base, and has an operating arm, 12, behind the base, equal in length to the arms, 8 and 9, and disposed so as to bisect the angle between the arms, 10 and 11. The arms, 10 and 11, are equal to each other and N /2 units in length between the center of rotation and loops, 7, which are formed at the extremities.

It will be evident that the loci of the center of loops 7, on cranks, 5 and 6, are circles, 13 and 14, respectively, of radius, N; and the locus of the center of loops, 7, on. cranks, 10 and 11, is a circle, 15, having a radius, N /2.

At the lower corners of square, 2, screw eyes or the like, 16 and 17, are inserted in the base with their axes at right angles, as shown. A flexible filament, 18, such as string or thread, is then threaded through the eyes, 7, 16 and 17, in the direction of the arrows shown thereon, and a weight,

19, is suspended in the loop, 20, below the screw eye, 17, as shown.

In adjusting the mechanism, the cranks,

10 and 11, may be turned until loops, 7 at the extremities thereof, coincide with corners, 21 and 22, respectively, of square, 2; and cranks, 5 and 6, should be turned. until they are horizontal, with the loops, 7 at points, 28 and 24, respectively. When the cranks are in this relative position, the arms, 8, 9 and 12, should be substantially parallel and may be connected by the operating bar, 25. i

It will be apparent from a consideration of the drawing, Figs. 1 and 2, that the filament, 18, appears to cross itself at right angles at point, 26, which forms the vertex of a right triangle having the base, 27, of 

